# 第 24937 題：有限群同態的核 [返回所在分頁 125](https://ocme.evemisslab.com/zh-Hant/questions/page/125/) [← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-foundations/#q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0012) 本頁是已完成第二對話 AI 數理與中英語義覆核的教學詳解，只支持本題明示的模型與前提。沒有人工審查或新 Lean 證明，也不提升原題或 MKO 的 Canonical 真值狀態。 R0048-24937 · q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0012 ## 原題與已知條件 完整來源／目標Cayley table與complete total map逐對同態核對。操作=kernel-homomorphism-qualification；資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"source_identity":0,"target_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"target_identity":0,"mapping":[0,13,12,11,10,9,8,7,6,5,4,3,2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — 完整來源／目標Cayley table與complete total map逐對同態核對。操作=kernel-homomorphism-qualification；資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"source_identity":0,"target_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"target_identity":0,"mapping":[0,13,12,11,10,9,8,7,6,5,4,3,2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 ## 定義與適用範圍 沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。 - [mko-finite-group-homomorphism-kernel](https://ocme.evemisslab.com/zh-Hant/mko/mko-finite-group-homomorphism-kernel/) ## 逐步推導 S001 · implies操作前 source roles = [kernel-homomorphism-qualification] 操作後 derived = [[source_order, target_order, mapping, product_law_rows, homomorphism, first_failed_pair_or_null, certificate]] 條件：無 直接列來源完整欄序，不需JavaScript；原題、布林旗標、數學物件與非聲稱保持分層。 步驟識別與依賴規則：source_ordered_fields_without_JS · 依賴：G001 S002 · implies操作前 source roles = [Kernel ORIGINAL SOURCE group, 64, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]], 0] 操作後 derived = [14, [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5], [6, 6, 6, 6], [7, 7, 7, 7], [8, 8, 8, 8], [9, 9, 9, 9], [10, 10, 10, 10], [11, 11, 11, 11], [12, 12, 12, 12], [13, 13, 13, 13]], 是] 條件：無 先驗完整n×n閉合表與實際identity標籤，非預設0。mod44上限32，mod45上限64；同一carrier不能混入另一表。 步驟識別與依賴規則：Group_complete_Cayley_signature_actual_identity · 依賴：G001, S001 S003 · implies操作前 source roles = [Kernel ORIGINAL SOURCE group, 14, FOR EVERY x,y,z in0..n-1] 操作後 derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 2744, 是] 條件：無 矩陣(x,y)逐全部z核(xy)z=x(yz)，故涵蓋全部n³三元組，不是抽樣。表已在前步完整列出，不重印數百萬同義查表項。 步驟識別與依賴規則：Group_ALL_associativity_triples_compact_complete_pair_matrix · 依賴：G001, S002 S004 · implies操作前 source roles = [Kernel ORIGINAL SOURCE group, 0] 操作後 derived = [[0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [[0, 0, 0, 0], [1, 13, 0, 0], [2, 12, 0, 0], [3, 11, 0, 0], [4, 10, 0, 0], [5, 9, 0, 0], [6, 8, 0, 0], [7, 7, 0, 0], [8, 6, 0, 0], [9, 5, 0, 0], [10, 4, 0, 0], [11, 3, 0, 0], [12, 2, 0, 0], [13, 1, 0, 0]], 是] 條件：無 每個元素的左、右逆都要回到同一實際identity；結合律使兩側逆唯一。這才完成群前提。 步驟識別與依賴規則：Group_ALL_two_sided_inverses · 依賴：G001, S003 S005 · implies操作前 source roles = [Kernel ORIGINAL TARGET group, 64, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]], 0] 操作後 derived = [14, [[0, 0, 0, 0], [1, 1, 1, 1], [2, 2, 2, 2], [3, 3, 3, 3], [4, 4, 4, 4], [5, 5, 5, 5], [6, 6, 6, 6], [7, 7, 7, 7], [8, 8, 8, 8], [9, 9, 9, 9], [10, 10, 10, 10], [11, 11, 11, 11], [12, 12, 12, 12], [13, 13, 13, 13]], 是] 條件：無 先驗完整n×n閉合表與實際identity標籤，非預設0。mod44上限32，mod45上限64；同一carrier不能混入另一表。 步驟識別與依賴規則：Group_complete_Cayley_signature_actual_identity · 依賴：G001, S004 S006 · implies操作前 source roles = [Kernel ORIGINAL TARGET group, 14, FOR EVERY x,y,z in0..n-1] 操作後 derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 2744, 是] 條件：無 矩陣(x,y)逐全部z核(xy)z=x(yz)，故涵蓋全部n³三元組，不是抽樣。表已在前步完整列出，不重印數百萬同義查表項。 步驟識別與依賴規則：Group_ALL_associativity_triples_compact_complete_pair_matrix · 依賴：G001, S005 S007 · implies操作前 source roles = [Kernel ORIGINAL TARGET group, 0] 操作後 derived = [[0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [[0, 0, 0, 0], [1, 13, 0, 0], [2, 12, 0, 0], [3, 11, 0, 0], [4, 10, 0, 0], [5, 9, 0, 0], [6, 8, 0, 0], [7, 7, 0, 0], [8, 6, 0, 0], [9, 5, 0, 0], [10, 4, 0, 0], [11, 3, 0, 0], [12, 2, 0, 0], [13, 1, 0, 0]], 是] 條件：無 每個元素的左、右逆都要回到同一實際identity；結合律使兩側逆唯一。這才完成群前提。 步驟識別與依賴規則：Group_ALL_two_sided_inverses · 依賴：G001, S006 S008 · implies操作前 source roles = [[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]], [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]], [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]] 操作後 derived = [[[0, 0, 0, 0, 是], [0, 1, 13, 13, 是], [0, 2, 12, 12, 是], [0, 3, 11, 11, 是], [0, 4, 10, 10, 是], [0, 5, 9, 9, 是], [0, 6, 8, 8, 是], [0, 7, 7, 7, 是], [0, 8, 6, 6, 是], [0, 9, 5, 5, 是], [0, 10, 4, 4, 是], [0, 11, 3, 3, 是], [0, 12, 2, 2, 是], [0, 13, 1, 1, 是], [1, 0, 13, 13, 是], [1, 1, 12, 12, 是], [1, 2, 11, 11, 是], [1, 3, 10, 10, 是], [1, 4, 9, 9, 是], [1, 5, 8, 8, 是], [1, 6, 7, 7, 是], [1, 7, 6, 6, 是], [1, 8, 5, 5, 是], [1, 9, 4, 4, 是], [1, 10, 3, 3, 是], [1, 11, 2, 2, 是], [1, 12, 1, 1, 是], [1, 13, 0, 0, 是], [2, 0, 12, 12, 是], [2, 1, 11, 11, 是], [2, 2, 10, 10, 是], [2, 3, 9, 9, 是], [2, 4, 8, 8, 是], [2, 5, 7, 7, 是], [2, 6, 6, 6, 是], [2, 7, 5, 5, 是], [2, 8, 4, 4, 是], [2, 9, 3, 3, 是], [2, 10, 2, 2, 是], [2, 11, 1, 1, 是], [2, 12, 0, 0, 是], [2, 13, 13, 13, 是], [3, 0, 11, 11, 是], [3, 1, 10, 10, 是], [3, 2, 9, 9, 是], [3, 3, 8, 8, 是], [3, 4, 7, 7, 是], [3, 5, 6, 6, 是], [3, 6, 5, 5, 是], [3, 7, 4, 4, 是], [3, 8, 3, 3, 是], [3, 9, 2, 2, 是], [3, 10, 1, 1, 是], [3, 11, 0, 0, 是], [3, 12, 13, 13, 是], [3, 13, 12, 12, 是], [4, 0, 10, 10, 是], [4, 1, 9, 9, 是], [4, 2, 8, 8, 是], [4, 3, 7, 7, 是], [4, 4, 6, 6, 是], [4, 5, 5, 5, 是], [4, 6, 4, 4, 是], [4, 7, 3, 3, 是], [4, 8, 2, 2, 是], [4, 9, 1, 1, 是], [4, 10, 0, 0, 是], [4, 11, 13, 13, 是], [4, 12, 12, 12, 是], [4, 13, 11, 11, 是], [5, 0, 9, 9, 是], [5, 1, 8, 8, 是], [5, 2, 7, 7, 是], [5, 3, 6, 6, 是], [5, 4, 5, 5, 是], [5, 5, 4, 4, 是], [5, 6, 3, 3, 是], [5, 7, 2, 2, 是], [5, 8, 1, 1, 是], [5, 9, 0, 0, 是], [5, 10, 13, 13, 是], [5, 11, 12, 12, 是], [5, 12, 11, 11, 是], [5, 13, 10, 10, 是], [6, 0, 8, 8, 是], [6, 1, 7, 7, 是], [6, 2, 6, 6, 是], [6, 3, 5, 5, 是], [6, 4, 4, 4, 是], [6, 5, 3, 3, 是], [6, 6, 2, 2, 是], [6, 7, 1, 1, 是], [6, 8, 0, 0, 是], [6, 9, 13, 13, 是], [6, 10, 12, 12, 是], [6, 11, 11, 11, 是], [6, 12, 10, 10, 是], [6, 13, 9, 9, 是], [7, 0, 7, 7, 是], [7, 1, 6, 6, 是], [7, 2, 5, 5, 是], [7, 3, 4, 4, 是], [7, 4, 3, 3, 是], [7, 5, 2, 2, 是], [7, 6, 1, 1, 是], [7, 7, 0, 0, 是], [7, 8, 13, 13, 是], [7, 9, 12, 12, 是], [7, 10, 11, 11, 是], [7, 11, 10, 10, 是], [7, 12, 9, 9, 是], [7, 13, 8, 8, 是], [8, 0, 6, 6, 是], [8, 1, 5, 5, 是], [8, 2, 4, 4, 是], [8, 3, 3, 3, 是], [8, 4, 2, 2, 是], [8, 5, 1, 1, 是], [8, 6, 0, 0, 是], [8, 7, 13, 13, 是], [8, 8, 12, 12, 是], [8, 9, 11, 11, 是], [8, 10, 10, 10, 是], [8, 11, 9, 9, 是], [8, 12, 8, 8, 是], [8, 13, 7, 7, 是], [9, 0, 5, 5, 是], [9, 1, 4, 4, 是], [9, 2, 3, 3, 是], [9, 3, 2, 2, 是], [9, 4, 1, 1, 是], [9, 5, 0, 0, 是], [9, 6, 13, 13, 是], [9, 7, 12, 12, 是], [9, 8, 11, 11, 是], [9, 9, 10, 10, 是], [9, 10, 9, 9, 是], [9, 11, 8, 8, 是], [9, 12, 7, 7, 是], [9, 13, 6, 6, 是], [10, 0, 4, 4, 是], [10, 1, 3, 3, 是], [10, 2, 2, 2, 是], [10, 3, 1, 1, 是], [10, 4, 0, 0, 是], [10, 5, 13, 13, 是], [10, 6, 12, 12, 是], [10, 7, 11, 11, 是], [10, 8, 10, 10, 是], [10, 9, 9, 9, 是], [10, 10, 8, 8, 是], [10, 11, 7, 7, 是], [10, 12, 6, 6, 是], [10, 13, 5, 5, 是], [11, 0, 3, 3, 是], [11, 1, 2, 2, 是], [11, 2, 1, 1, 是], [11, 3, 0, 0, 是], [11, 4, 13, 13, 是], [11, 5, 12, 12, 是], [11, 6, 11, 11, 是], [11, 7, 10, 10, 是], [11, 8, 9, 9, 是], [11, 9, 8, 8, 是], [11, 10, 7, 7, 是], [11, 11, 6, 6, 是], [11, 12, 5, 5, 是], [11, 13, 4, 4, 是], [12, 0, 2, 2, 是], [12, 1, 1, 1, 是], [12, 2, 0, 0, 是], [12, 3, 13, 13, 是], [12, 4, 12, 12, 是], [12, 5, 11, 11, 是], [12, 6, 10, 10, 是], [12, 7, 9, 9, 是], [12, 8, 8, 8, 是], [12, 9, 7, 7, 是], [12, 10, 6, 6, 是], [12, 11, 5, 5, 是], [12, 12, 4, 4, 是], [12, 13, 3, 3, 是], [13, 0, 1, 1, 是], [13, 1, 0, 0, 是], [13, 2, 13, 13, 是], [13, 3, 12, 12, 是], [13, 4, 11, 11, 是], [13, 5, 10, 10, 是], [13, 6, 9, 9, 是], [13, 7, 8, 8, 是], [13, 8, 7, 7, 是], [13, 9, 6, 6, 是], [13, 10, 5, 5, 是], [13, 11, 4, 4, 是], [13, 12, 3, 3, 是], [13, 13, 2, 2, 是]], 是, null] 條件：無 先對同一source/target每對(x,y)驗f(xy)=f(x)f(y)，保首failed row/null。total map不是homomorphism；失敗即擋所有kernel定理，不把內部fallback當真正identity preimage。 步驟識別與依賴規則：Kernel_complete_TOTAL_map_ALL_product_pairs_before_theorems · 依賴：G001, S007 ## 逐步反向核對 - S008 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S004 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 - S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。 ## 結論 (14, 14, [0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [[0, 0, 0, 0, 是], [0, 1, 13, 13, 是], [0, 2, 12, 12, 是], [0, 3, 11, 11, 是], [0, 4, 10, 10, 是], [0, 5, 9, 9, 是], [0, 6, 8, 8, 是], [0, 7, 7, 7, 是], [0, 8, 6, 6, 是], [0, 9, 5, 5, 是], [0, 10, 4, 4, 是], [0, 11, 3, 3, 是], [0, 12, 2, 2, 是], [0, 13, 1, 1, 是], [1, 0, 13, 13, 是], [1, 1, 12, 12, 是], [1, 2, 11, 11, 是], [1, 3, 10, 10, 是], [1, 4, 9, 9, 是], [1, 5, 8, 8, 是], [1, 6, 7, 7, 是], [1, 7, 6, 6, 是], [1, 8, 5, 5, 是], [1, 9, 4, 4, 是], [1, 10, 3, 3, 是], [1, 11, 2, 2, 是], [1, 12, 1, 1, 是], [1, 13, 0, 0, 是], [2, 0, 12, 12, 是], [2, 1, 11, 11, 是], [2, 2, 10, 10, 是], [2, 3, 9, 9, 是], [2, 4, 8, 8, 是], [2, 5, 7, 7, 是], [2, 6, 6, 6, 是], [2, 7, 5, 5, 是], [2, 8, 4, 4, 是], [2, 9, 3, 3, 是], [2, 10, 2, 2, 是], [2, 11, 1, 1, 是], [2, 12, 0, 0, 是], [2, 13, 13, 13, 是], [3, 0, 11, 11, 是], [3, 1, 10, 10, 是], [3, 2, 9, 9, 是], [3, 3, 8, 8, 是], [3, 4, 7, 7, 是], [3, 5, 6, 6, 是], [3, 6, 5, 5, 是], [3, 7, 4, 4, 是], [3, 8, 3, 3, 是], [3, 9, 2, 2, 是], [3, 10, 1, 1, 是], [3, 11, 0, 0, 是], [3, 12, 13, 13, 是], [3, 13, 12, 12, 是], [4, 0, 10, 10, 是], [4, 1, 9, 9, 是], [4, 2, 8, 8, 是], [4, 3, 7, 7, 是], [4, 4, 6, 6, 是], [4, 5, 5, 5, 是], [4, 6, 4, 4, 是], [4, 7, 3, 3, 是], [4, 8, 2, 2, 是], [4, 9, 1, 1, 是], [4, 10, 0, 0, 是], [4, 11, 13, 13, 是], [4, 12, 12, 12, 是], [4, 13, 11, 11, 是], [5, 0, 9, 9, 是], [5, 1, 8, 8, 是], [5, 2, 7, 7, 是], [5, 3, 6, 6, 是], [5, 4, 5, 5, 是], [5, 5, 4, 4, 是], [5, 6, 3, 3, 是], [5, 7, 2, 2, 是], [5, 8, 1, 1, 是], [5, 9, 0, 0, 是], [5, 10, 13, 13, 是], [5, 11, 12, 12, 是], [5, 12, 11, 11, 是], [5, 13, 10, 10, 是], [6, 0, 8, 8, 是], [6, 1, 7, 7, 是], [6, 2, 6, 6, 是], [6, 3, 5, 5, 是], [6, 4, 4, 4, 是], [6, 5, 3, 3, 是], [6, 6, 2, 2, 是], [6, 7, 1, 1, 是], [6, 8, 0, 0, 是], [6, 9, 13, 13, 是], [6, 10, 12, 12, 是], [6, 11, 11, 11, 是], [6, 12, 10, 10, 是], [6, 13, 9, 9, 是], [7, 0, 7, 7, 是], [7, 1, 6, 6, 是], [7, 2, 5, 5, 是], [7, 3, 4, 4, 是], [7, 4, 3, 3, 是], [7, 5, 2, 2, 是], [7, 6, 1, 1, 是], [7, 7, 0, 0, 是], [7, 8, 13, 13, 是], [7, 9, 12, 12, 是], [7, 10, 11, 11, 是], [7, 11, 10, 10, 是], [7, 12, 9, 9, 是], [7, 13, 8, 8, 是], [8, 0, 6, 6, 是], [8, 1, 5, 5, 是], [8, 2, 4, 4, 是], [8, 3, 3, 3, 是], [8, 4, 2, 2, 是], [8, 5, 1, 1, 是], [8, 6, 0, 0, 是], [8, 7, 13, 13, 是], [8, 8, 12, 12, 是], [8, 9, 11, 11, 是], [8, 10, 10, 10, 是], [8, 11, 9, 9, 是], [8, 12, 8, 8, 是], [8, 13, 7, 7, 是], [9, 0, 5, 5, 是], [9, 1, 4, 4, 是], [9, 2, 3, 3, 是], [9, 3, 2, 2, 是], [9, 4, 1, 1, 是], [9, 5, 0, 0, 是], [9, 6, 13, 13, 是], [9, 7, 12, 12, 是], [9, 8, 11, 11, 是], [9, 9, 10, 10, 是], [9, 10, 9, 9, 是], [9, 11, 8, 8, 是], [9, 12, 7, 7, 是], [9, 13, 6, 6, 是], [10, 0, 4, 4, 是], [10, 1, 3, 3, 是], [10, 2, 2, 2, 是], [10, 3, 1, 1, 是], [10, 4, 0, 0, 是], [10, 5, 13, 13, 是], [10, 6, 12, 12, 是], [10, 7, 11, 11, 是], [10, 8, 10, 10, 是], [10, 9, 9, 9, 是], [10, 10, 8, 8, 是], [10, 11, 7, 7, 是], [10, 12, 6, 6, 是], [10, 13, 5, 5, 是], [11, 0, 3, 3, 是], [11, 1, 2, 2, 是], [11, 2, 1, 1, 是], [11, 3, 0, 0, 是], [11, 4, 13, 13, 是], [11, 5, 12, 12, 是], [11, 6, 11, 11, 是], [11, 7, 10, 10, 是], [11, 8, 9, 9, 是], [11, 9, 8, 8, 是], [11, 10, 7, 7, 是], [11, 11, 6, 6, 是], [11, 12, 5, 5, 是], [11, 13, 4, 4, 是], [12, 0, 2, 2, 是], [12, 1, 1, 1, 是], [12, 2, 0, 0, 是], [12, 3, 13, 13, 是], [12, 4, 12, 12, 是], [12, 5, 11, 11, 是], [12, 6, 10, 10, 是], [12, 7, 9, 9, 是], [12, 8, 8, 8, 是], [12, 9, 7, 7, 是], [12, 10, 6, 6, 是], [12, 11, 5, 5, 是], [12, 12, 4, 4, 是], [12, 13, 3, 3, 是], [13, 0, 1, 1, 是], [13, 1, 0, 0, 是], [13, 2, 13, 13, 是], [13, 3, 12, 12, 是], [13, 4, 11, 11, 是], [13, 5, 10, 10, 是], [13, 6, 9, 9, 是], [13, 7, 8, 8, 是], [13, 8, 7, 7, 是], [13, 9, 6, 6, 是], [13, 10, 5, 5, 是], [13, 11, 4, 4, 是], [13, 12, 3, 3, 是], [13, 13, 2, 2, 是]], 是, null, complete_total_map_satisfies_every_product_pair) 依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。 ## 本題覆核與來源綁定 覆核日期：2026-10-26 原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。 來源雜湊與覆核憑證 - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: 9322b015aea93bd3fe33a23759905b2e3241dfa73b11aa10a32c66e43f884b11 - candidate record SHA-256: 5f23f66da4a00738ca6731a037cdd0108e8d2883828721b967a40787bb3ab853 - semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0 - question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9 - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0012.json)